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Walther MA279 Fall2018 topic7

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-PDF Version: [[File:Proj.pdf]]
-== MA 279, Fall 2018 ==
-== Fractals and Music ==
-Daksh Jotwani, Daniel Atallah, Noah Talbot, Zoe Phillips
-=== Introduction ===
-“If music is invented to mimic a certain harmony in nature, the mountains are sounds; rivers are lyrics”
-- Zhi-Yuan Su and Tzuyin Wu
-We have always been fascinated by the infinite number of patterns surrounding our environment. Patterns are a huge part of our daily observations; from uniformly distributed branches on a tree, to clouds colliding to form familiar objects, we seek to find structure in everything we see, hear, and feel around us.
-A subset of patterns that we observe has been classified as fractals. Fractals are generally depicted visually, since we primarily rely on vision to observe our surroundings. These patterns, however, are also  observed in a multitude of natural phenomena, and we seek to explore aural examples of them.
-Music is a sequence of temporally structured sounds which are sonically appealing to the human ear. Since music is sequential, aural, and possesses a well-defined structure, we believe that exploring the structural patterns of music could lead to observation of some interesting fractals and applications of them. Therefore, we have chosen to explore and document some fascinating fractals which have been observed in the field of music.
-=== Background ===
-Fractals are infinite self-similar patterns. These patterns are generated by non-terminating sequences, and are usually defined recursively. Fractals are well-observed in nature, and hence are very familiar, as shown by the example below:
-[[File:fig1.]]

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